Problem: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{2.64\times 10^{-3}}{8.0\times 10^{0}}} =\ ?$
Solution: Start by collecting the significands and exponents. $ {\dfrac {{2.64} \times {10^{-3}}} {{8.0} \times {10^{0}}} = {\dfrac{2.64}{8.0}} \times {\dfrac{10^{-3}}{10^{0}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.33} \times {10^{-3 \,-\, 0}}$ $= {0.33} \times {10^{-3}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.33}$ is the same as ${3.3 \div 10}$, or ${3.3 \times 10^{-1}}$. $ = {3.3 \times 10^{-1}} \times {10^{-3}} $ $ = 3.3 \times 10^{{-1} + {-3}} $ $= 3.3\times 10^{-4}$